Question

These questions are to be answered using MATLAB. I only need #3 answered, but #1 provides information (like initial velocity, etc.) required for the questions. I think I have it done, but I'd like to see if there are other ways to use MATLAB for this question.

PROJECTILES The distance a projectile travels when fired at an angle 8 is a function of time and can be divided into horizontal and vertical distances. Horizontal (1) = 1.V.cos(0) Vertical(t) = 1• V..sin(6) - Žgt? where Horizontal is the distance traveled in the x direction, Vertical is the distance traveled in the y direction, V. is the initial velocity, 8 is the acceleration due to gravity, 9.8 m/s, and is time in seconds. 1. For the projectile just described and fired at an initial velocity of 100 m/s and a launch angle of /4 (45°), find the distance traveled both horizon- tally and vertically in the x and y directions) for times from 0 to 20 seconds. Graph horizontal distance versus time on one plot, and in a new figure window plot vertical distance versus time (time on the x-axis). Do not forget a title and labels. 2. In a new figure window, plot horizontal distance on the x-axis and vertical distance on the y-axis. 3. Calculate new vectors for the vertical (v1, U'y, and 03) and horizontal (h, hy, and hz) distance traveled, assuming launch angles of /3,7/4,7/6. In a new figure window, graph horizontal distance on the xaxis and vertical distance on the y-axis, for all three cases. (You will have three lines.) Make one line solid, one dashed, and one dotted. Add a legend to identify which line is which

Answer 1

1 - clc, clear, close all 2 3 4 5 - %% PART 1. g = 9.8; 3 m/s^2 Vo = 100; m/s theta = pi/4; radians t = linspace(0,20,100); $s. Using 100 points. The more points, the better 6 - 7 - 8 9 - Horizontal = t * Vo * cos (theta); Vertical = t * VO * sin(theta) - 0.5 * g * t.^2; 10 - EP 11 12 - 13 - 14 15 - figure, plot(t, Horizontal), title('Plot of Horizontal distance vs time') xlabel('time [s]'), ylabel ('Horizontal distance [m] '), grid on figure, plot(t, Vertical), title('Plot of Vertical distance vs time') xlabel('time [3]'), ylabel('Verticle distance [m]'),grid on 16 - 17 18 19 - %% PART 2 figure, plot (Horizontal, Vertical) title('Plot of Verticle vs Horizontal distances') xlabel('Horizontal distance [m]'), vlabel('Verticle distance [m]'),grid on 20 21 22

23 24 25 & PART 3 $ initialize the launch angles thetal = pi/3; theta2 pi/4; theta3 = pi/6; 26 27 - w w N N N N N N 28 29 30 computing the vertical distances for different values of theta vl = t * V * sin(thetal) - 0.5 *g* t. 2; v2 = t * V * sin(theta2) - 0.5 * g * t. 2; v3 = t * Vo * sin(theta 3) - 0.5 * g t.^2; 31 * 33 34 - 35 36 37 38 computing the horizontal distances for different values of theta hi = t * Vo * cos (thetal); h2 = t * Vo * cos (theta2); h3 = t * V * cos (theta3); www 39 40 41 $ plotting results figure, plot (hi,vi,'-', h2, v2,'--',h3, v3,'.'),grid on title('Plot of Verticle vs Horizontal distances, varying launch angies') legend ('theta = pi/3', 'theta = pi/4', 'theta = pi/6') xlabel ('Horizontal distance [m]'), vlabel('Vertical distance [m]') 42 43

Plot of Horizontal distance vs time 1500 1000 Horizontal distance [m] 500 0 0 2 4 6 8 10 12 14 16 18 20 time [s]

Plot of Vertical distance vs time 300 200 100 o Verticle distance [m] -200 -300 -400 -500 -600 0 4 6 8 10 12 14 16 18 N 20 time [s]

Plot of Verticle vs Horizontal distances 300 200 100 0 Verticle distance [m] -200 -300 -400 -500 -600 0 1500 500 1000 Horizontal distance [m]

Plot of Verticle vs Horizontal distances, varying launch angles 400 theta = pi/3 theta = pi/4 200 theta = pi/6 -200 Vertical distance [m] -400 -600 -800 -1000 0 200 400 1400 1600 1800 600 800 1000 1200 Horizontal distance [m]

clc,clear,close all

%% PART 1.
g = 9.8; % m/s^2
Vo = 100; % m/s
theta = pi/4; % radians
t = linspace(0,20,100); % s. Using 100 points. The more points, the better

Horizontal = t * Vo * cos(theta);
Vertical = t * Vo * sin(theta) - 0.5 * g * t.^2;

figure,plot(t,Horizontal),title('Plot of Horizontal distance vs time')
xlabel('time [s]'),ylabel('Horizontal distance [m] '),grid on

figure,plot(t,Vertical),title('Plot of Vertical distance vs time')
xlabel('time [s]'),ylabel('Verticle distance [m]'),grid on

%% PART 2
figure,plot(Horizontal,Vertical)
title('Plot of Verticle vs Horizontal distances')
xlabel('Horizontal distance [m]'),ylabel('Verticle distance [m]'),grid on

%% PART 3
% initialize the launch angles
theta1 = pi/3;
theta2 = pi/4;
theta3 = pi/6;

% computing the vertical distances for different values of theta
v1 = t * Vo * sin(theta1) - 0.5 * g * t.^2;
v2 = t * Vo * sin(theta2) - 0.5 * g * t.^2;
v3 = t * Vo * sin(theta3) - 0.5 * g * t.^2;

% computing the horizontal distances for different values of theta
h1 = t * Vo * cos(theta1);
h2 = t * Vo * cos(theta2);
h3 = t * Vo * cos(theta3);

% plotting results
figure,plot(h1,v1,'-',h2,v2,'--',h3,v3,'.'),grid on
title('Plot of Verticle vs Horizontal distances, varying launch angles')
legend('theta = pi/3','theta = pi/4','theta = pi/6')
xlabel('Horizontal distance [m]'),ylabel('Vertical distance [m]')

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